Sums and Gaussian Vectors / Edition 1

by Vadim Yurinsky

Overview

Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.

Product Details

ISBN-13:	9783540603115
Publisher:	Springer Berlin Heidelberg
Publication date:	11/29/1995
Series:	Lecture Notes in Mathematics , #1617
Edition description:	1995
Pages:	312
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Gaussian measures in euclidean space.- Seminorms of Gaussian vectors in infinite dimensions.- Inequalities for seminorms: Sums of independent random vectors.- Rough asymptotics of large deviations.- Gaussian and related approximations for distributions of sums.- Fine asymptotics of moderate deviations.